The Greens are jubilant after sweeping through Labour heartlands in last week’s elections, winning Norwich, Hastings, Waltham Forest, Hackney and Lewisham, while becoming the largest party in Haringey and Lambeth too. At the same time, there are reports that Zack Polanski is “plotting” to water down the Green policy platform. That’s not quite true. As leader of an admirably democratic party, Polanski doesn’t set the policy programme, and he knows it. It’s in the hands of the members. But his comments do speak to a real debate in the Green party: how to consolidate its newfound success and extend the coalition so it can replace Labour from the left.

To put things very simply, there are two emerging positions. The maximalists, often newer members who have cut their teeth in protest politics and social movements, want to seize on the radicalism of the moment, pushing controversial policies that grab attention and move the Overton window further left. Then there are the moderates – often longstanding members and councillors, branch chairs or party staffers – who are generally supportive of the politics but worry that seeming too radical or out there will hurt the party’s chances electorally. Employing the Ming vase strategy, they want to tiptoe the Greens’ newfound popularity over the finish line.

Both these camps are half right. The maximalists are alive to the sheer crisis and instability of 21st-century politics. When support for the status quo is at such a low ebb, what is deemed unrealistic or impossible can suddenly become reality. Just look at the polls: who would have predicted Reform UK polling first and the Greens often polling second less than two years after a Labour landslide? They are also in tune with how attentional our politics has become: what Anton Jäger calls an era of “hyperpolitics” in which everyone is politicised through consuming content rather than being a member of a political party. In this context, causing controversy, defining the news agenda and winning salience for your issue become a huge chunk of the battle.

And yet the moderates’ caution has some merit. Broadening the Greens’ coalition means appealing to a diverse set of voters who are united on the cost of living and climate but less so on other issues that activists might hold dear. Radicalism for its own sake, without attention to what is actually popular, will be punished.

My argument is for a third way: a strategic radicalism that focuses on issues and policies that are both radical and popular. This means starting from our principles – not with a focus group – then identifying where the people and party agree, and relentlessly focusing on that overlap. And, when we’re asked about our more unpopular stances, explaining patiently, not apologising and getting back to more favourable terrain.

The Greens have plenty of grist for this populist mill: rent caps, 10:1 wage pay ratios, the requisitioning of empty properties, wealth taxes, abolishing the House of Lords – the list goes on. Anything that pits them against a corporate and political elite and on the side of the people is popular. The key is to do it with verve and swagger, provoking fights with Labour, Reform and big corporations that force the media to pay attention.

Enter Hannah Spencer. Her opposition to MPs drinking on the job went mega-viral last month, prompting backlash from Nigel Farage and Labour backbenchers – “fags and beer” are one of the things that make the job “seem [a] tiny bit normal”, said one Labour MP – while YouGov has 76% of the public in agreement with Spencer. New York’s mayor, Zohran Mamdani, is a master at this too. His city-run grocery-store plan left the New York Post frothing yet attracted majority support and kept him in the news for weeks when many voters didn’t know who he was.

There are plenty of fronts. Getting all Green MPs to take an average worker’s wage – following the example of Labour-left MP Nadia Whittome – and promising to make MPs of all parties do the same would set Westminster WhatsApp groups ablaze. A 100% tax on oil company “Iran war profits” to fund lower energy bills would marry anger against foreign wars, against Donald Trump and against big corporates. No party is seen as the “cost of living” party yet, polling suggests. With Reform doubling down on immigration, proposing emergency price controls on food and basic goods would help the Greens win this mantle.

Either we grab attention and dominate the news or we talk about boob hypnosis ad nauseam. That’s the choice. It will require an all-party effort. Polanski’s advisers will tend towards moderation: they’re the ones tiptoeing the Ming vase. They’ll need to defy that instinct, take calculated risks and judge their work by how many fights we can have on our terms. Green members have power too – at conference and locally. Our job is to push motions that benefit the party as a whole rather than treating the Greens as a vehicle for our pet causes.

As Polanski suggested, reforming the policymaking process could help. Die Linke in Germany and the Belgian Workers’ party (PTB) have combined member-led conferences with extensive door-to-door consultation, producing manifestos shaped by voters’ concerns as well as activists’ desires. That is the Green party’s sweet spot: be democratic enough to stay radical but rooted enough to become popular.

• Joe Todd is co-host of the Life of the Party podcast and writes the New Party, Old Problems Substack